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Reflection and Transmission of Equatorial Rossby Waves

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  • 1 Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
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Abstract

The interaction of equatorial Rossby waves with a western boundary perforated with one or more narrow gaps is investigated using a shallow-water numerical model and supporting theory. It is found that very little of the incident energy flux is reflected into eastward-propagating equatorial Kelvin waves provided that at least one gap is located within approximately a deformation radius of the equator. Because of the circulation theorem around an island, the existence of a second gap off the equator reduces the reflection of short Rossby waves and enhances the transmission of the incident energy into the western basin. The westward energy transmitted past the easternmost island is further reduced upon encountering islands to the west, even if these islands are located entirely within the “shadow” of the easternmost island. A localized patch of wind forcing was also used to generate low-frequency Rossby waves for cases with island configurations representative of the western equatorial Pacific. For both idealized islands and a coastline based on the 200-m isobath, the amount of incident energy reflected into Kelvin waves depends on both the duration of the wind event and the meridional decay scale of the anomalous winds. For wind events of 2-yr duration with a meridional decay scale of 700 km, the reflected energy is 37% of the incident flux, and the energy transmitted into the Indian Ocean is approximately 10% of the incident flux, very close to that predicted by previous theories. For shorter wind events or winds confined more closely to the equator the reflected energy is significantly less.

Corresponding author address: Dr. Michael A. Spall, Woods Hole Oceanographic Institution, WHOI MS #21, 360 Woods Hole Road, Woods Hole, MA 02543. Email: mspall@whoi.edu

Abstract

The interaction of equatorial Rossby waves with a western boundary perforated with one or more narrow gaps is investigated using a shallow-water numerical model and supporting theory. It is found that very little of the incident energy flux is reflected into eastward-propagating equatorial Kelvin waves provided that at least one gap is located within approximately a deformation radius of the equator. Because of the circulation theorem around an island, the existence of a second gap off the equator reduces the reflection of short Rossby waves and enhances the transmission of the incident energy into the western basin. The westward energy transmitted past the easternmost island is further reduced upon encountering islands to the west, even if these islands are located entirely within the “shadow” of the easternmost island. A localized patch of wind forcing was also used to generate low-frequency Rossby waves for cases with island configurations representative of the western equatorial Pacific. For both idealized islands and a coastline based on the 200-m isobath, the amount of incident energy reflected into Kelvin waves depends on both the duration of the wind event and the meridional decay scale of the anomalous winds. For wind events of 2-yr duration with a meridional decay scale of 700 km, the reflected energy is 37% of the incident flux, and the energy transmitted into the Indian Ocean is approximately 10% of the incident flux, very close to that predicted by previous theories. For shorter wind events or winds confined more closely to the equator the reflected energy is significantly less.

Corresponding author address: Dr. Michael A. Spall, Woods Hole Oceanographic Institution, WHOI MS #21, 360 Woods Hole Road, Woods Hole, MA 02543. Email: mspall@whoi.edu

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